A Bayesian Statistical Study of Bianchi Type-I Universe in $f(R,T^ψ)$ Modified Gravity

TL;DR

The paper investigates an anisotropic cosmology in $f(R,T^{\psi})$ gravity by adopting a first-order formalism with $H = W(\psi)$ and analyzing the scalar potential $V(\psi)$ for a locally rotationally symmetric Bianchi type-I metric. It constrains the model using Bayesian MCMC against OHD, BAO, and Pantheon data, obtaining best-fit parameters with favorable $\chi^{2}_{\rm red}$ and information criteria, and showing consistency with late-time cosmic acceleration. Om$(z)$ diagnostics further reveal quintessence-like behavior of dark energy and a close, data-consistent expansion history relative to $\Lambda$CDM. Overall, the study demonstrates that an anisotropic, geometry–matter–scalar field coupling in $f(R,T^{\psi})$ gravity can reproduce observed cosmological dynamics while providing a robust statistical fit to current datasets.

Abstract

We have examined the cosmological actions of LRS (Locally Rationally Symmetric) Bianchi type-I universe model in $f(R,T^ψ)$ gravity. For this, we have estimated the Hubble parameter, the effective equation of state parameter ($ω^{eff}$), and the potential of the scalar field as a function of time using equation $H = W(ψ)$. The graphical representation of the potential function $V(ψ)$ with respect to cosmic time t is described. This study explores the dynamical properties of a Bianchi Type-I universe by utilizing Bayesian statistical techniques to constrain the model parameters and evaluate the viability of anisotropic cosmology under extended matter-geometry couplings. Also, we have applied the Markov Chain Monte Carlo (MCMC) mechanism on the derived $H(z)$ model by using observational Hubble data (OHD), the Baryon Acoustic Oscillation (BAO) dataset, and the Pantheon dataset. From the confidence-level contours and best-fit parameter values obtained, along with the corresponding reduced $χ^{2}$, it is evident that the model aligns strongly with observational data, demonstrating statistical stability and consistency in describing late-time cosmic acceleration. Likewise, the error analyses presented in this research, including a comparison between the $Λ$CDM cosmology and the reconstructed $H(z)$ model, confirm the model's compatibility with current observations by yielding a reliable and accurate account of the universe's expansion history.

Figures (10)

• Figure 1: Evolution of the scalar-field $\psi$ as a function of cosmic time t for different values of the anisotropy parameter n.
• Figure 2: Evolution of the scalar-field potential V($\psi$)as a function of cosmic time t for different values of the anisotropy parameter n.
• Figure 3: Confidence contours and marginalized posterior distributions for the parameters $\ln s$, $\log b_{1}$, $\log \alpha$, and $\mu$ obtained from the Hubble (OHD) dataset.
• Figure 4: Joint posterior distributions and confidence contours for the model parameters obtained from BAO data.
• Figure 5: MCMC-based posterior distributions for parameters $c_1$, $\mu$, $\log \alpha$, and $n$ using the Pantheon Type Ia Supernova dataset.